Civil Engineering - MCQ Practice Questions

Stiffness matrix [K] is symmetric (reciprocal theorem) and positive definite for stable structures without rigid body movements.

For planar frames: DI = (m + r) - 2j, where 2j accounts for 2 equilibrium equations per joint in 2D.

Castigliano's first theorem: ∂U/∂P = δ, where U is strain energy and δ is deflection at point of load P.

Williot-Mohr diagram graphically represents the deflected shape showing displaced position of all joints in a truss.

For SS beam with central load, maximum deflection occurs at x = L/√3 ≈ 0.577L from support, not at center due to boundary conditions.

For a parabolic arch under UDL, the horizontal thrust H = wL²/(8f), where f is rise. The thrust decreases with increase in rise-to-span ratio. Optimal ratio is $\frac{1}{2}$ for many design considerations.

Maximum bending moment occurs at the section where shear force is zero (point of contraflexure). For moving loads, position varies but this principle always applies.

Flexibility coefficients for non-uniform beams require integration accounting for variable EI along the length.

Global stiffness matrix is assembled by superposition of element stiffness matrices after coordinate transformation.

Plastic collapse occurs when sufficient plastic hinges develop to convert the structure into a mechanism, allowing unbounded deformation.

Beam elements use cubic Hermite shape functions to ensure C¹ continuity (displacement and slope continuity).

DSI = (r + 3m) - 2j = (4 + 3×3) - 2×4 = 13 - 8 = 3 for this portal frame configuration.

C3A reacts rapidly with water and is responsible for flash setting. Gypsum is added to control this reaction.

Abrams' Law states that compressive strength decreases exponentially with increase in water-cement ratio.

SCC requires slump flow between 600-800 mm to flow and compact under its own weight without vibration.

For a parabolic arch with UDL and three hinges optimally placed, bending moment can be zero throughout if h = wL²/8.

Load factor (collapse multiplier) = Collapse load/Service load. It measures how much the load can be increased before collapse.

Unit load method (virtual work) requires applying a unit load (or moment for slope) at the point where deflection (or slope) is required.

FEA uses the principle of minimum potential energy (variational principle) to assemble global stiffness matrix from element stiffness matrices.

Eigenvalues in buckling analysis represent the critical load multipliers at which the column becomes unstable and buckles.